关键词: 二元双偶极值码, 自同构, 生成矩阵, 等价, 循环矩阵

Abstract:

By regarding the extremal selfdual doublyeven binary codes with type of 7(8,0) as a polynomial over GF(2)n , we can factorize it to a contract code and even weight polynomials, and construct extremal selfdual doublyeven binary codes with type of 7(8,0) by shorter codes. The possible generator matrix of the codes is given. Matlab procedure implementation shows that, because the minimal distance is 12, codes with type of 7(8,0) do not exist when the dimension of E1(σ)* is 2;and there are 75 selfdual doublyeven binary codes with type of 7(8,0) when the dimension of E1(σ)* is 4. We discuss the similarities of the extremal selfdual doublyeven binary codes with length of 56 to 70,  and obtain the generator matrix and classification. So the generator matrices and classification of the extremal selfdual doublyeven binary codes with length between 50 and 70 can be solved completely.Key words:

Key words: extremal selfdual doublyeven binary codes;automorphism;generator matrix;equivalence;cyclic matrix